Magnetic geodesics on surfaces with singularities

TL;DR

This paper investigates the behavior of magnetic geodesics on surfaces with singularities, showing that generically they avoid points with lightlike tangent planes, supported by numerical solutions for closed magnetic geodesics.

Contribution

It provides a generic result about magnetic geodesics avoiding certain singular points and includes numerical analysis of closed magnetic geodesics.

Findings

Magnetic geodesics tend to turn away from lightlike tangent points

Numerical solutions illustrate behavior of closed magnetic geodesics

Results apply to surfaces with singularities

Abstract

We prove that, generically, magnetic geodesics on surfaces will turn away from points with lightlike tangent planes, and we motivate our result with numerical solutions for closed magnetic geodesics.